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Worksheet: Introduction to Exponential Decay

In this worksheet, we will practice using the properties of exponential decay to solve real-world and mathematical problems and differentiating between types of decay.

Q1:

The production of a gold mine is decreasing with a rate of annually. Given that the mine’s production was 6 400 kg
in the first year, determine its production in the sixth year, giving your answer the nearest integer.

Q2:

A car was valued at $38000 in the year 2007. By 2013, the value had depreciated to $11000. Assuming continuous depreciation at the same rate, find, to the nearest dollar, the value of the car in 2017.

Q3:

The Asian elephant population 𝑡 years after the year 1900 is given by
𝑃=100000⋅0.25𝑡/100.

What was the Asian elephant population in 1900?

A50000

B25000

C200000

D100000

E15000

According to this model, by what percentage has the Asian elephant population decreased over a century?

A75%

B15%

C50%

D25%

E55%

Q4:

The function 𝑦=𝐴𝑏𝑥 represents a 15% decay in each period that 𝑥 measures. What is the value of 𝑏?

Q5:

Determine whether the data shown exhibits growth or decay, stating whether it is linear or exponential.

𝑥

−2

−1

0

1

2

3

𝑦

2400

1200

600

300

150

75

Alinear growth

Bexponential growth

Clinear decay

Dexponential decay

Q6:

Determine whether the data shown exhibits growth or decay, stating whether it is linear or exponential.

𝑥

0

1

2

3

𝑦

2970

990

330

110

Alinear growth

Bexponential growth

Clinear decay

Dexponential decay

Q7:

Which of the functions below represents exponential decay?

A𝑓(𝑥)=7𝑥

B𝑓(𝑥)=138−𝑥

C𝑓(𝑥)=68𝑥

D𝑓(𝑥)=1033𝑥

Q8:

Which of the functions below represents exponential decay?

A𝑓(𝑥)=65𝑥

B𝑓(𝑥)=121−𝑥

C𝑓(𝑥)=16𝑥

D𝑓(𝑥)=451𝑥

Q9:

Which of the functions below represents exponential decay?

A𝑓(𝑥)=54𝑥

B𝑓(𝑥)=148−𝑥

C𝑓(𝑥)=65𝑥

D𝑓(𝑥)=2329𝑥

Q10:

The value of a car depreciates by 8% per year. A new car costs $20000.
Write an expression for the car’s value in dollars when it is 𝑡 years old.